Determinants of hemoglobin level and time to default from Highly Active Antiretroviral Therapy (HAART) for adult clients living with HIV under treatment; a retrospective cohort study design

HIV/AIDS is one of the most devastating infectious diseases affecting humankind all over the world and its impact goes beyond public health problems. This study was conducted to investigate the joint predictors of hemoglobin level and time to default from treatment for adult clients living with HIV/AIDS under HAART at the University of Gondar Comprehensive and Specialized Hospital, North-west Ethiopia. The study was conducted using a retrospective cohort design from the medical records of 403 randomly selected adult clients living with HIV whose follow-ups were from September 2015 to March 2022. Hemoglobin level was projected using Sahli’s acid-hematin method. Hence, the hemoglobin tube was filled with N/10 hydrochloric acid up to 2 g % marking and the graduated tube was placed in Sahli’s hemoglobin meter. The blood samples were collected using the finger-pick method, considering 22 G disposable needles. The health staff did this. From a total of 403 adult patients living with HIV/AIDS included in the current study, about 44.2% defaulted from therapy. The overall mean and median estimated survival time of adult clients under study were 44.3 and 42 months respectively. The patient’s lymphocyte count (AHR = 0.7498, 95% CI: (0.7411: 0.7587), p-value < 0.01), The weight of adult patients living with HIV/AIDS (AHR = 0.9741, 95% CI: (0.9736: 0.9747), p-value = 0.012), sex of adult clients (AHR = 0.6019, 95% CI: (0.5979, 0.6059), p-value < 0.01), WHO stages III compared to Stage I (AHR = 1.4073, 95% CI: (1.3262, 1.5078), p-value < 0.01), poor adherence level (AHR = 0.2796, 95% CI: (0.2082, 0.3705) and p-value < 0.01), bedridden patients (AHR = 1.5346, 95% CI: (1.4199, 1.6495), p-value = 0.008), and opportunistic infections (AHR = 0.2237, 95% CI: (0.0248, 0.4740), p-value = 0.004) had significant effect on both hemoglobin level and time to default from treatment. Similarly, other co-morbidity conditions, disclosure status of the HIV disease, and tobacco and alcohol addiction had a significant effect on the variables of interest. The estimate of the association parameter in the slope value of Hgb level and time default was negative, indicating that the Hgb level increased as the hazard of defaulting from treatment decreased. A patient with abnormal BMI like underweight, overweight, or obese was negatively associated with the risk of anemia (lower hemoglobin level). As a recommendation, more attention should be given to those patients with abnormal BMI, patients with other co-morbidity conditions, patients with opportunistic infections, and low lymphocytes, and bedridden and ambulatory patients. Health-related education should be given to adult clients living with HIV/AIDS to be good adherents for medical treatment.

www.nature.com/scientificreports/Human immunodeficiency virus/Acquired immune deficiency syndrome (HIV/AIDS) is one of the most disturbing infectious diseases affecting humankind overall the world and its impact goes beyond public health problems 1 .Since, the beginning of the epidemic, about 85.6 million adults have been infected with the HIV virus and among these, about 40.4 million people have been died because of HIV related disease.Globally, about 39 million people were living with HIV at the end of 2022 and of these 630,000 were died from HIV-related causes and 1.3 million people acquired HIV 2 .
HIV/AIDS is also a leading cause of morbidity and mortality in Sub-Saharan African country 2 .Hence, about two-thirds of the world's adult clients living with HIV/AIDS (about 23.5 million or 69%) belonged to Sub-Saharan Africa in the end of 2022 1,3 .Ethiopia, one of the Sub-Saharan African countries, has large percentage of population living with HIV/AIDS and under treatment 4 .HIV remains a crucial public health concern in the country with a prevalence rate of 0.9% ranging from 0.1 to 4.8% among adults 4 .
The Amhara region, one of the eleven regions in the country, is a pandemic area of the HIV disease where large adult clients living with the HIV/AIDS 4,5 .Even though HIV prevalence in Ethiopia decreased from year to year, the issue is still a significant epidemic burden in the region 6,7 .Hence, the region is at the 5th rank with prevalence rate of 4.1% in the country related to HIV infection among urban adults 8 .
The progression of HIV leads to a decrease in blood hemoglobin levels and is substantially associated with a decrease in the survival time of patients or waiting time patients under treatment 9 .Low hemoglobin levels are a common hematological problem among adults living with HIV.It is related to a higher risk of developing opportunistic infections 10 .The hematological parameters (hemoglobin level), and waiting time of patients under treatment can be significantly improved by early HAART initiation 11 .However, many adult clients living with the virus are defaulting from Highly Active Antiretroviral Therapy (HAART), and some are completely rejecting HAART and further leading to a substantial decrease in hematological parameters 11,12 .
Defaulting from HAART occurred because of transferring to another health centers for different reasons, defaulting because of death of patients or defaulting because of ignorance /forgotten the appointment given by the health staff.Defaulting also related to be non-medication adherence including taking pills 12 .Adult clients living with the HIV/AIDS has short waiting time under treatment if he/she defaulted from treatment and defaulter patients have decreasing survival time under treatment.
Most of the studies, conducted previously are longitudinal or survival, conducted separately 9 .Hence, a study had been conducted on blood hemoglobin measurement as a predictive indicator for the progression of HIV/ AIDS in resource-limited settings 9 .Another study had been also conducted with a separate survival time to explore possible risk factors for time-to-default of adult clients living with HIV/AIDS using the Cox Proportional Hazards (Cox-PH) model 12 .
Such studies did not investigate the relationships between the two response variables namely hemoglobin level and time to default at the same time.Joint modeling of longitudinal and survival data incorporates all information about the two responses simultaneously and provides valid and efficient inferences for the given data.Hence, the joint model is very essential to overcome the problem of escaping the association between the longitudinal and survival responses.It is also important to reduce the biases of parameter estimates accounted for the association between the two responses 13 .
As far as the authors' knowledge are concerned, there is a scarcity of studies about joint analysis of hemoglobin (Hgb) level and time to default from HAART in the study area.Therefore, the main objective of this study was to identify predictors for hemoglobin level and time to default from HAART jointly for adult clients living with HIV/AIDS under HAART at the University of Gondar comprehensive Specialized Hospital, the Amhara region, north-west Ethiopia.

Study area and study design
This study was conducted at the University of Gondar Comprehensive Specialized Hospital Amhara region, North-west Ethiopia.The hospital belongs to the University of Gondar and it is a specialized, referral and teaching hospital.Hence, many patients from district hospitals in the catchment area are referred to this hospital and about 5000 HIV-infected patients at any ages are under treatment in this treatment center.The study area was selected because of a large number of adult clients living with HIV/AIDS registered HAART.An institutionalbased retrospective cohort study design was carried out to retrieve relevant information from the medical records of adult clients living with HIV/AIDS.

Study population, study period, and sampling procedures and inclusion criterion
The study population for this study was all medical records of adult clients living with HIV/AIDS, treated at the hospital whose follow-ups were from September 2015 to March 2022.The source of data in this study was a secondary source obtained by reviewing medical records of adult clients living with HIV/AIDS treated under the follow-up periods.
All the primary data from the respondents were collected by the health staff for treatment purpose and documented in organized manner with their own identification number within the hospital.During data collection from the patients, anthropometry was conducted using the standard protocol.Hence, height in meter was recorded without shoes by the measuring tape which was mounted on the wall.Weight in kilo grams was taken on Duchess weighing scale with light clothes and without shoes.BMI in kilograms/metre 2 was calculated using Quetelet formula as shown below 14  A systematic random sampling technique was applied to select random files/charts form the documentation section.All the variables and respected values (data) from each file has been collected by the health staff.The data collection format was developed by the investigators in consultation with the health staff working in the ART section of the hospital.In collecting secondary data from the charts of patients, name of each patient was not declared in the data collection sheet rather, the identification number of patients was indicated corresponding to other variables included under study.
The study included all adult clients living with HIV/AIDS attending with a minimum of two visiting times for a longitudinal response, adult clients living with HIV/AIDS patients whose ages were at least 15 years, and patients who had started their treatment within study periods were included under this study.HIV patients with ages less than 15 years old or HIV-patients under treatment with less than two visiting times and adult clients living with HIV/AIDS with incomplete data were excluded in the current study.

Sample size determination
The appropriate sample size determination formula used in this study was based on 14 which is given by: n = d p(defualt) the total number of defaulters ( d ) can be found by using d = , where n is the required number of adult clients living to be include in this study, α is the level of significance or the size of the critical region in hypothesis testing and it is taken as 5% in this study, β is the power of the test with value 80% taken for this case.From the standard normal distribution table z α 2 and z β the upper α/2 and upper β points are given as 1.96 and 0.84 respectively.Hence, the total sample size included under this study was 403.

Quality of data
In a retrospective cohort study design, the data collection procedures were based on the patient's charts and electronic database system.In order to ensure the quality of the collected data, one-day of intensive training was given to data extractors.Pilate test was conducted on 25 randomly selected charts before a formal data collection procedures started.The necessary amendments were conducted to the final data extraction format for completeness and consistency of the data.

Dependent variables
The two response variables under this investigation were hemoglobin (Hgb) level per deciliter of blood and time to default from HAART.The longitudinal biomarker (Hgb level) for adult clients living with HIV/AIDS was measured at every 6 months interval starting from baseline, 6, 12 …72 months.The survival time for each patient was also measured in months by subtracting the month of starting HAART from the month of event existence.

Explanatory variables
The explanatory variables in the current study, selected based on the previous related literature, were weight in kg, BMI in kg/m 2 , age in years, sex, functional status, residence area, religion, marital status, education level, occupation, disclosure status, alcohol addiction, tobacco addiction, WHO Clinical stage, ART regiment, medication adherence, TB co-infection, Opportunistic infections (OIs), Other Comorbid Condition (OCC) and visiting times in a month.For further information on the categories of explanatory variables in this study, one can refer to Table 1 in the results section.
Measures of selected variables: Hemoglobin level was computed using Sahli's acid hematin method.Hence, the hemoglobin tube was filled with N/10 hydrochloric acid up to 2 g % marking and the graduated tube was placed in Sahli's hemoglobin meter and the samples of blood were collected using finger pick method, considering 22 G disposable needles.Then the sample of blood was dropped in to Sahli's tube up to 20 ML marking and the sample of blood and hydrochloric acid were mixed using stirrer.In order to change the mixture in to acid hematin, the process was conducted for about 5 min.The acid hematin was diluted using pure/distilled water with dropper until it matched with the standard color plates of comparator.The unit for results obtained from this procedure was read as g/dl and the level of hemoglobin was projected up to 0.1 g/dl.The patient was categorized as anemic if the hemoglobin level was at most 12 g/dl.
Body Mass Index (BMI) was considered as continuous variables ( any value with unit kg/m 2 ) and based on Quetlet's index these continuous values were categorized under-weight if the BMI was less than 18.5 kg/m 2 , healthy weight, if the BMI was 18.5-25 kg/m 2 , overweight, if the BMI was 25-30 kg/m 2 and obesity, if the BMI was at least 30 kg/m 2. .Correlation between hemoglobin concentration and BMI was assessed using Pearson's correlation coefficient.

The generalized linear mixed effects model
In longitudinal data analysis, the outcome variable was measured repeatedly over time for each of the participants/subjects.In this case, there were two sources of variations: within and between subject variations.Modeling within patient variation allows us to study changes over time while modeling between-patient variation allows understand changes between patients/subjects 14 .Random effects were used to generate correlation structures between repeated measurements in longitudinal studies [14][15][16] .The linear mixed effect model was used to model the repeatedly measured longitudinal data that quantifies the relationships between a continuous dependent variable and various covariates 17  Let Y ij (i = 1,2,…,n; j = 1,2,…, n i ) be the hemoglobin level of patient i at follow up visit time j; Y i = (y i1 , y i2 , . . ...., y ini ) T a random vector; X T i1 be an n i × p design matrix of fixed effects for patient i that is associated with the p-dimensional vector β i of fixed effects; and Z T i1 be an n i × q design matrix of random effects for patient i that is associated with the q dimensional vector ν i of patient specific random effects.Then, if the conditional distribution of Yi given ν i is from the exponential family, the generalized linear mixed effects model for Yi can be written as 17 : where g(.) is the link function that is completely specified by the conditional of y i in the exponential family.Since, the response of the current investigation was continuous, the unit link function was used in this study.
Semi-parametric survival model: One of the most popular types of regression models in the case of semiparametric is the Cox proportional hazards (Cox PH) regression model 15 .The Cox PH model consists of two parts; the hazard function often denoted by describing how the hazard (risk) changes over time at baseline levels of covariate and the covariate with exponential of product with their coefficients 15 .The Cox PH semi-parametric model has a common choice for the time-to-event model.
The hazard function is a measure of the probability of failure during a very small interval, assuming that the individual has survived at the beginning of the interval 16 .The hazard function describes the concept of the risk of an outcome (defaulter) in an interval after time t, conditional on the subject having survived to time t 16 .
Method of data analysis: R software of version 4.3 was used for data analysis.In data analysis, exploratory data analysis, individual profiles plot, and exploring mean structure were conducted.Similarly, the covariance structures were compared and the one with the smallest AIC and BIC were selected.Hence, among the different covariance structures, un-structure was selected for the current study.Missing data management was also conducted using multiple data imputation techniques.

Ethics approval and consent to participate
All methods were performed in accordance with the ethical standards as laid down in the Declaration of Helsinki and its later amendments or comparable ethical standards.Informed consent was obtained from all the

Results
The socio-demographic, behavioral, and clinical characteristics of baseline categorical variables together with the observed survival process are described in Tables 1 and 2. Out of 403 study subjects/participants, 64.5% were female and 35.5% were male adult clients living with HIV/AIDS.The majority of the participants in the current study were at working functional status (68.2%) and orthodox religious followers (89.8%), and around half of the patients (45.2%) were between the age group 25-34 years (refer to Table 1).Regarding adherence status, about 56.3% of poor adherents, 50.6% of fair adherents, and 41.7% of good adherents have been defaulted from HAART (refer to Table 2).
The baseline continuous characteristics of participants included in this study are indicated in Table 3. Table 3 indicates that the mean hematocrit of 403 participants under study was 37.7% with its corresponding standard deviation of 4.50% and with minimum and maximum hematocrit of 20.1% and 54.3% respectively.The mean weight of patients was 46.94 kg. with a corresponding standard deviation of 10.9 kg and the mean of WBC, RBC, and Platelet cell count of adult clients living with HIV/AIDS with their corresponding standard deviation were 6.01 (1.88)10^3/µl , 4.17 (1.35), 10^6/µl , and 286.93 (95.25) 10^3/µl respectively(Reference to Table 3).
Longitudinal linear mixed effect models: The mean hemoglobin level of adult clients living with HIV/AIDS under HAART at baseline was 12.87 g/dl with a corresponding standard deviation of 3.0392 g/dl.Smaller mean Hgb levels of adult clients living with HIV/AIDS were observed at the baseline period and increased continuously as visiting time increased (72 months).
Before proceeding to the longitudinal data model building, the possible covariates were selected for the multivariable linear mixed model at a 25% level of significance in the univariate data analysis.
Model comparisons of linear mixed-effects model: Different candidate models with different random effects were considered for longitudinal measures of the Hgb level of the adult clients living with HIV/AIDS.The most appropriate random effect model for the longitudinal measures was selected using the deviance information criteria (DIC).Hence, random intercepts and random slopes for the Hgb level under the full model were selected because of the smaller value of DIC.Joint model results: Joint model of the two response variables was conducted considering different latent processes for the repetitive measures of hemoglobin level.The joint model was conducted assuming that there are homogeneous and heterogeneous variances for the variable of interest.Hence, the longitudinal sub-model was described using conventional generalized linear mixed effects model including patient-explicit variances.On the other hand, the time to default from the HAART sub-model was fitted using a Cox proportional hazard (Cox PH) model and the two sub-models were correlated considering common covariates.The joint model of the two response variables is indicated in Table 4.For the table to be manageable within one page, all rows with insignificant variables are deleted in this joint data analysis.
Table 4 indicates that the mean fixed effect intercept estimated coefficient in the longitudinal sub-model was 11.38 g/dl, given that the other covariates are constant.The result indicates that visiting time was a significant covariate for longitudinal responses.Hence as visiting time increased by one month, the expected hemoglobin level was increased by 0.0475 g/dl, and the hazard of defaulting patients from treatment was decreased by 32.5%, holding all other covariates constant (p-value = 0.002).
As the body mass index of a patient increased by one kg/m 2 (for low BMI patients) the expected hemoglobin level of the patients was increased by 0.0896 and the corresponding hazard of defaulting from the treatment was decreased by 8.4%, given the other covariates constant (p-value < 0.01).Compared low BMI patients with healthy BMI, the expected hemoglobin level of low BMI was 0.0896 times that of healthy BMI given the other covariates constant (p-value < 0.01).Similarly, comparing high BMI with health BMI, the expected level of hemoglobin for high BMI was 0.076 times that of healthy BMI (p-value < 0.01).Hence, the current study indicates that abnormal BMI (very low and very high BMI) had negative correlation with hemoglobin level.
The patient's Platelet cell count had a significant effect on both Hgb level and time to default.As the patient's platelet cell count increased by a 10^3/ml, the expected Hgb level was increased by 0.0757 g/dl and the corresponding hazard of defaulting from treatment was decreased by 7.3%, holding the other covariates constant (p-value = 0.001).The patient's lymphocyte count had a significant effect on both Hgb level and time to default.As the lymphocyte count of a patient increased by one unit, the expected Hgb was increased by 0.2879 g/dl, and the corresponding hazard of defaulting from the treatment was decreased by 25.1% holding for other covariates constant (AHR = 0.7498, 95% CI: (0.7411: 0.7587), p-value < 0.01).
The weight of adult clients living with HIV had a significant effect on their Hgb level and time to default.As the patient's weight increased by one kg, the expected level of Hgb was increased by 0.0262 g/dl and the corresponding hazard of defaulting from the treatment was decreased by 2.6%, given the other covariates constant (AHR = 0.9741, 95% CI: (0.9736: 0.9747), p-value = 0.012).
Comparing female with male patients, the expected level of Hgb of females was increased by 0.5077 g/dl and the corresponding hazard of defaulting from the treatment was decreased by 40%, given the other covariates constant (AHR = 0.6019, 95% CI: (0.5979: 0.6059), p-value < 0.01).
The result in Table 4 also indicates that WHO stages had a significant effect on the variables of interest.Hence, comparing WHO stage II with WHO stage I, the expected Hgb level of WHO stage II was decreased by 0.5766 as compared to WHO stage I, and the corresponding hazard of defaulted from the treatment for WHO stage II patients was increased by 56%, given the other covariates constant (AHR = 1.5618, 95% CI: (1.4474, 1.7195), p-value < 0.01).Similarly, comparing the WHO stage III with WHO stage I, the expected level of Hgb for WHO stage III was decreased by 0.8982 g/dl, and the corresponding hazard of defaulted from the treatment by WHO stage III patients was increased by 40.7% given the other conditions constant (AHR = 1.4073, 95% CI: (1.3262, 1.5078), p-value < 0.01).
Adherence had a significant effect on the variables of interest.Comparing fair adherent patients with poor adherent patients, the expected level of fair adherent patients was increased by 0.2719 g/dl and the corresponding hazard of defaulting from the treatment was decreased by 24.8%, given the other conditions constant (AHR = 0.7619, 95% CI: (0.6313, 0.9036), p-value = 0.006).In the same way, comparing good adherent patients with poor adherent patients, the expected level of Hgb for good adherent patients was 1.2742 g/dl times that of poor adherent patients, and the corresponding hazard of defaulting from the treatment was decreased by 72.1% as compared to that of poor adherent patients, given the other conditions constant (AHR = 0.2796, 95% CI: (0.2082, 0.3705) and p-value < 0.01).
HIV functional status was another variable that significantly affected the variable of interest.Hence, the comparing ambulatory patients with patients at working status, the expected level of Hgb for ambulatory adult clients living with HIV/AIDS was decreased by 0.0291 g/dl and the corresponding hazard of defaulting from treatment was increased by 2.9% (AHR = 1.0295, 95% CI: (1.0064, 1.2433), p-value = 0.004).Similarly, the expected level of Hgb for bedridden adult clients living with HIV/AIDS was decreased by 0.4283 g/dl as compared to patients with working status, and the corresponding hazard of defaulting from the treatment was increased by 53%, given the other conditions constant (AHR = 1.5346, 95% CI: (1.4199, 1.6495), p-value = 0.008).
Opportunistic infections significantly affected the variables of interest.Hence, comparing those adult clients living with HIV/AIDS who had opportunistic infections with those without infections, the expected level of Hgb for patients without opportunistic infection was increased by 0.2019 g/dl, and the corresponding hazard of defaulting from treatment was decreased by 97.5% as compared to adult client living with HIV/AIDS who had opportunistic infections, given the other conditions constant (AHR = 0.2237, 95% CI: (0.0248, 0.4740), p-value = 0.004).
Similarly, the variables such as other co-morbidity conditions, disclosure status of the HIV disease, tobacco and alcohol addiction had a significant effect on the variables of interest.

Discussions
The association parameter estimated at the joint model analysis was considerably different from zero and this is an indication of the correlation between the two sub-models.The estimate of the association parameter due to the slope of Hgb was negative.This means that the slope of Hgb is negatively associated with the hazard of default.This finding was consistent with one of the previously conducted studies 15,16 .
Visiting time of patients was positively associated with the expected value of Hgb level and negatively associated with the hazard to default from the treatment.Hence, as the visiting time of a patient increased the corresponding expected value of Hgb level increased and the hazard of defaulting from treatment decreased.The potential reason for this might be the fact that proper follow-ups lead to the progression of Hgb and this further encourages the patients strictly follow his/her treatment.This result was in line with the previous studies 15,17 .
Hematocrit has a great association with the level of hemoglobin and the time to default from treatment.This result indicates that a higher value of hematocrit leads to a higher level of homogony.However, those patients with higher hematocrit had a lower risk of defaulting from treatment.This finding is in line with study conducted in Nigeria 18 .
The result of this study showed that the body mass index (BMI) of patients was a significant predictor for the response, Hgb level.The result in the current study indicates that a patient with Abnormal BMI like underweight (low BMI), overweight or obese, were associated with the risk of anemia and there was a negative association between hemoglobin concentration and abnormal BMI among patients under treatment.This result is consistent with one of the previous study 18 .This result was also consistent with the study conducted by 15 .The result of this study implied that the hazard of defaulters decreases with the increasing BMI for patients with low BMI but the hazard of defaulters increase with decreasing of BMI for patients with very high BMI.This result is supported by another study 19 .
The result obtained in this study also indicates that the platelet cell count was a statistically significant factor for the longitudinal Hgb level of adult clients living with HIV/AIDS.The result indicates that the expected Hgb level increases with the increasing rate of platelet cell count of patients.This study is consistent with other studies 20,21 .
HIV disease functional status of patients had statistically significant effects on hemoglobin level of patients under treatment.Hence, adult clients living with HIV/AIDS under bedridden functional status have lower expected level of Hgb as compared to working status.This study is consistent with another study 22 .Regarding the hazard of defaulting from treatment of adult clients living with HIV/AIDS, the result indicates that bedridden adult clients living with HIV/AIDS have a higher risk of defaulting as compared to that of working status.This result is consistent with the studies conducted in South-west Ethiopia 23,24 .
The result in current study also indicates that the weight of adult clients living with HIV/AIDS had positive correlation with the expected level of Hemoglobin level.Hence, the expected level of Hgb increased with the increasing rate of weight of patients.On the other hand, weight of patients and the hazard of defaulting from treatment for adult clients living with HIV/AIDS were negatively associated.This result is supported by the previous study 24 .
ART adherence was another factor significantly associated with Hgb level and the hazard of defaulting from the treatment.Good ART adherent patients have higher expected level of Hgb as compared to poor adherent patients.The result of this study indicates that good and fair adherent HIV-positive patients had a lower risk of defaulting from HAART as compared to poor adherent patients.This finding is consistence with other studies 25,26 .
This study also indicates that WHO clinical stage-III and IV adult HIV-positive patients have lower Hgb than patients with WHO clinical stage-I patients.This result was supported by other studies 27,28 .This result is also consistent with a study done by 29 .Similarly, the WHO clinical stage of adult HIV-positive patients was a significant risk factor for the hazard of defaulting from ART treatment.This study was consistent with another study 30 .
Regarding tobacco addiction, the Hgb level of tobacco-addicted adult HIV-positive patients was significantly lower in number as compared to non-addicted patients.This result is in line with other previously conducted studies done at Arba Minch, Ethiopia 17,31 .The result in the current study also indicates that the hazard of defaulting from treatment for tobacco addicted patients was higher as compared to non-addicted patients.This result is consistent with a study conducted by Deribe et al. 32 .
The patient with alcohol addiction has a lower level of Hgb.This result is contradicted by the study done in Ethiopia 33,34 .In this study, alcohol-addicted patients have a lower expected level of Hgb than non-addicted patients.The risk of defaulting from treatment is higher among alcohol-addicted patients as compared with nonalcohol addicted patients.The result of this study is consistent with a study conducted by 35 .Similarly, patients with a higher lymphocyte count have higher Hgb levels and consistent with another study conducted by 36 .
Sex has a significant association with the variables of interests namely Hgb level and the risk of defaulting from treatment.Female adult clients living with HIV/AIDS have higher Hgb levels and a lower risk of defaulting from the treatment.The result of this study was consistent with another study conducted by 37 .
The age of patients has a great role for the variation of level of Hgb and risk of defaulting from the treatment.This result is inconsistence with a study conducted in Ethiopia 38 .Under this study, patients' history of OIs had a significant association with their default time, where patients who had a history of OIs had a higher risk of defaulting as compared to patients without history OIs.

Conclusion
In conclusion, the results of both separate and joint model analyses were conducted in this study.The coefficient of association parameter was different from zero and statistically significant.The two responses were negatively correlated in such a way that an increase in Hgb leads to a decrease in the hazard of defaulting from the treatment.Among the predictor variables, BMI was significant for the longitudinal outcome variables namely hemoglobin level.Hence, a patient with Abnormal BMI like underweight, overweight or obese, were associated with the risk of anemia and there was a negative association between hemoglobin concentration and abnormal BMI among patients under treatment.
Among the covariates, visiting time, hematocrit, BMI, platelet cell count, lymphocyte count, sex, WHO clinical stage, functional status, OIs, tobacco addiction, alcohol addiction, disclosure status of the disease and adherence level of patients significantly affected both Hgb level and hazard of defaulting from the treatment.
AS a recommendation, the authors in current study recommended that health experts should conduct healthrelated education for patients to be good adherent for the prescribed medication and strict followers of their treatment.

Limitation of the study
This research is not without limitations.One of the limitations is that some variables such as nutritional status, income status, homeownership, viral load status, and other hematological parameters like Eosinophil, Neutrophil, and Basophil counts were not available on the patient's chart that might be associated with the Hgb level and risk of defaulting from the treatment.Having such additional variables may have additional information related to Hgb level and risk of defaulting from treatment.Hence, this study recommended future investigations including such variables.The research was conducted in a single center and this may be another limitation for the current investigation.Having additional centers may increase the information from the current study that may add value for policy implication.Hence, the authors recommend conducting further researches including other treatment centers for the current result to be more valid and consistent or to get additional information.

Table 1 .
Baseline socio-demographic and behavioral covariates of study participants.participantsor their legal guardian for the study.Hence, the experimental protocol was approved by the Bahir Dar University licensing committee.

Table 2 .
Baseline clinical variables of participants.

Table 3 .
Baseline socio-demographic and clinical continuous predictors.Std.deviation indicates standard deviation of continuous predictors.

Table 4 .
Joint model parameter estimates for HGB and time-to-event sub-models.